Efficient parallel branch-and-bound algorithm for constructing minimum ultrametric trees

Abstract

The construction of evolutionary trees is important for computational biology, especially for the development of biological taxonomies. The ultrametric tree ( UT) is a commonly used model for evolutionary trees assuming that the rate of evolution is constant (molecular clock hypothesis). However, the construction of minimum ultrametric trees ( MUTs, principle of minimum evolution) has been shown to be NP-hard even from a metric distance matrix. The branch-and-bound algorithm is generally used to solve a wide variety of NP-hard problems. In previous work, a sequential branch-and-bound algorithm for constructing MUTs ( BBU) was presented and the experimental results showed that it is useful for MUT construction. Hence, in this study, an efficient parallel branch-and-bound algorithm ( PBBU) for constructing MUTs or near- MUTs from a metric distance matrix was designed. A random data set as well as some practical data sets of Human + Chimpanzee Mitochondrial and Bacteriophage T7 DNAs were used to test the PBBU. The experimental results show that the PBBU found an optimal solution for 36 species on 16 PCs within a reasonable time. To the best of our knowledge, no algorithm has been found to solve this problem even for 25 species. Moreover, the PBBU achieved satisfying speed-up ratios for most of the test cases.